Lamine Yamal sparked the revival in the 30th minute, gliding past two defenders from a short corner before drilling a low cross for Bernal to convert from close range.
Atletico had a chance to ease the pressure but Ademola Lookman headed narrowly wide from a Marcos Llorente cross, with Barcelona doubling their lead shortly after, when defender Marc Pubill fouled Pedri inside the box in first-half stoppage time.
Raphinha sent the spot kick to the left as goalkeeper Juan Musso dived the other way.
Musso kept Atletico afloat after the break, producing a one-handed save to turn Pedri’s effort behind in the 54th minute and then denying Bernal from the edge of the area, before saving from Yamal twice.
The third goal arrived in the 72nd minute when Bernal volleyed home from a Joao Cancelo cross, leaving Barcelona one strike short of forcing extra time.
Instead, Atletico held on to progress and will face the winner of Wednesday’s other semi-final between Real Sociedad and Athletic Bilbao, with Sociedad carrying a 1-0 first-leg lead.
“A game like this makes you feel really proud of your team,” Barcelona captain Raphinha told Movistar Plus.
“If we continue playing like this, we’ll have a spectacular end to the season. I’m sure the fans are proud too, as demonstrated by what happened at the end of the match. We also know that we’re up against a team that defends its own.”
